Prove the identity (1/sinx - 1/tanx)^2 -= (1-cosx)/(1+cosx). ?
Prove the identity (1/sinx - 1/tanx)^2 -= (1-cosx)/(1+cosx).
Prove the identity
1 Answer
Mar 13, 2018
I would start with the left hand side, by rewriting in terms of sine and cosine.
LHS:
(1/sinx - 1/(sinx/cosx))^2
(1/sinx - cosx/sinx)^2
((1 - cosx)/sinx)^2
(1 -cosx)^2/sin^2x
Recall that
sin^2x +cos^2x = 1 -> sin^2x= 1- cos^2x .
(1 - cosx)^2/(1 - cos^2x)
Now do a little factoring.
((1 - cosx)(1 - cosx))/((1 + cosx)(1 - cosx))
(1 - cosx)/(1 + cosx)
We now see that LHS = RHS, therefore we've proven this identity.
Hopefully this helps!